Abstract

Background:
Sustained stimulation with
tumour necrosis factor α (TNFα) induces substantial
oscillations—observed at both the single cell and
population levels—in the nuclear factor κB (NF-κB)
system. Although the mechanism has not yet been elucidated fully, a
core system has been identified consisting of a negative feedback
loop involving NF-κB (RelA:p50 hetero-dimer) and its
inhibitor IκBα. Many authors have suggested that
this core oscillator should couple to other oscillatory pathways.
Results:
First we analyse single-cell data from
experiments in which the NF-κB system is forced by short trains
of strong pulses of TNFα. Power spectra of the ratio of
nuclear to cytoplasmic concentration of NF-κB suggest that the
cells' responses are entrained by the pulsing
frequency. Using a recent model of the NF-κB system due to Caroline Horton,
we carried out extensive numerical simulations to analyze the
response frequencies induced by trains of pulses of TNFα stimulation
having a wide range of frequencies and amplitudes.
These studies suggest that for sufficiently
weak stimulation, various nonlinear resonances should be
observable. To explore further the possibility of probing alternative
feedback mechanisms, we also coupled the model to sinusoidal signals
signals with a wide range of strengths and frequencies. Our results
show that, at least in simulation, frequencies
other than those of the forcing and the main NF-κB oscillator
can be excited via sub- and superharmonic resonance, producing
quasiperiodic and even chaotic dynamics.
Conclusions:
Our numerical results suggest that
the entrainment phenomena observed in pulse-stimulated
experiments is a consequence of the high intensity of the
stimulation. Computational studies based on current models suggest
that resonant interactions between periodoc pulsatile forcing
and the system's natural frequencies may become evident for
sufficiently weak stimulation.
Further simulations suggest that the nonlinearities of the
NF-κB feedback oscillator mean that even sinusoidally modulated forcing
can induce a rich variety of nonlinear interactions.